eMac Time and Date Resets

Does the eMac have a battery to keep settings when the machine is unplugged?
I have a 1.25Ghz model that I bought in August of last year. When I shutdown and unplug my machine, the Date is reset to December 31, 1969 and the Time/day to 7pm/Wednesday.

It isn't often that I either shut off the computer completely, much less unplug it, but it does seem a little odd that the Date and time are not kept.

Yes. There is a battery. It's on the main board near the RAM slot. Here's a link for a picture of the 800mhz board: http://www.lbodnar.dsl.pipex.com/eMac/pics/iMac-up.jpg. Other models are similar. It's unusual that a battery would go down that fast. They usually go for at least 3 years and 5 is not unusual. Before you spring for a new battery you might zap the PRAM, repair permissions and use a program like Preferential Treatment to check the pref files.